The first one is by searching through already existing chats. If we scroll down, at the very top it says "Search for people and groups". Give it one press to summon the keyboard, and the chats will be darkened in shadow.

In the example, the person we're looking for is located at the top of the results because he is our existing friend. There is also a list of people who are not our friends, but still, Facebook Messenger thinks that we might know them and might be searching for them.